Debutant Jon-Paul Pittman was particularly hard done by seeing a header cleared off the line and a strong penalty appeal waved away by referee Carl Boyeson. The 22-year-old signing from Crawley was impressive in an incident-packed first half and it was only the boot of City midfielder Dean Furman which prevented the striker from opening his Wycombe account with a header after just 13 minutes.
Bradford, who were looking to bag a third successive league win, made a lively start and Wanderers keeper Scott Shearer did well to push away a deflected shot from Nicky Law.
After 21 minutes Pittman was sent sprawling in the box by Matt Clarke's sliding challenge, but referee Boyeson waved away the appeals for a spot-kick.
Wycombe, who had only lost twice on their league travels this season, seemed to be taking a grip on the game when midfielder Matt Bloomfield wasted a great chance after half an hour.
Bloomfield looked to have too much time when the ball fell to him in the City box and with plenty of goal to aim at he dragged his 14-yard shot wide.
Pittman then went close with an overhead kick which flew just wide of the City goal before the visitors were hit with a sucker punch just before the break.
Bradford striker Peter Thorne calmly slid a square ball into the path of Jones two minutes before the interval and the on-loan winger lashed a left-foot shot into the top corner from 16 yards.
There were plenty of chances for both sides in an equalling entertaining second period, but the game was almost marred when Chris Zebroski made a careless high-footed challenge on Matt Clarke 12 minutes from time.
The midfielder was immediately shown a straight red and thankfully Clarke got up to finish the contest despite being kicked in the face.
The extra man meant City finished stronger and Nicky Law, Joe Colbeck and Paul Arnison all wasted chances to kill off the game.